The symbols 1 and 2are used to denote the extents of reaction for the first and

The symbols 1 and 2are used to denote the extents of

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Analysis of mole balance follows the extent of reaction method. The symbols 1 and 2 are used to denote the extents of reaction for the first and second reactions (Eq. 1.1), respectively. The mole balance of all chemical species are generally computed using the correlation as follows ´ n i = ´ n 0 + ν i ξ 1 where ´ n i is molar flow rate of the species i and I is the stoichiometric coefficient. Hence, the final flow rate from Figure 3.1 can be summarised as in Table 3.2 Table 3.1 Mole Balance for the Second Level of Decision Species Symbol Inlet Change Outlet Isobutylene A F A - 1 - 2 P A Oxygen B F B - 1 - 6 2 P B Methacrolein C 0 1 P c Carbon Dioxide D 0 4 2 P D Water E 0 + 1 -+4 1 P E In total, other than P B , there are 6 unknown variables. Information available to solve those variables can be detailed out as follows, based on the material and energy balance textbook (Felder & Rousseau, 2005) Number of unknown variables in the process 6 2 Independent reactions +2 5 equation of extent of reactions -5 Composition of Ratio of Isobutylene to Oxygen in the feed -1 Total (Variables can be calculate specifying two more information available) 2 The remaining information is obtained from the purge composition which will determine the ratio of excess for the whole process and design variable of the reactor which would be optimized based on the economic analysis. This purge composition is actually governing the feed ratio too through the mole balance of reactive unit. 3.1.1. Yield and Reaction Stoichiometry XY Methacrolein+Water (desired) X X ( 1 Y ) Carbon Dioxide+Water (undesired) IB (1-X) IB
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Table 3.1.1: Probability Sketch of the Process
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Table 3.2 Mole Balance in terms of conversion and yield for the Second Level of Decision Species Symbol Inlet Change Outlet Isobutylene A F A F A [-XY+X(1-Y)] F A [1-X] Oxygen B F B F A [-XY+6X(1-Y)] F A [6-6X+5XY] Methacrolein C 0 F A [XY] F A [XY] Carbon Dioxide D 0 F A [4X(1-Y)] F A [4X(1-Y)] Water E 0 F A [XY+4X(1-Y)] F A [XY+4(1-Y)] Total F A + F B F A (7+X-XY) From the probability sketch, we can obtain: P C = F A XY F A = P C XY F B = 6 P c XY Ratio of Isobutylene to Oxygen=1:6 1 + εX = No of moles output Noof molesinput 1 + εX = F A ( 7 + X XY ) F A + F B 1 + εX = F A ( 7 + X XY ) F A + 6 F A 1 + εX = 7 + X XY 7 Y = Rate of formationof desired Product Rateof consumption of Key Reactant Y = r C r A C A = C A 0 ( 1 X ) 1 + εX = 7 C A 0 ( 1 X ) 7 + X XY Y = r 1 A r 1 A +(− r 2 A ) C B = C A 0 ( 6 6 X + 5 XY ) 1 + εX = 7 C A 0 ( 6 6 X + 5 XY ) 7 + X XY
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Y = 1 1 +( r 2 A r 1 A ) Y =( 1 + k 2 C A 0.1 C B 0.1 k 1 C A 0.53 C B 0.37 ) 1 Y =( 1 + k 2 k 1 C A 0.43 C B 0.27 ) 1 Y =( 1 + k 2 k 1 ( 7 C A 0 ( 1 X ) 7 + X XY ) 0.43 7 C A 0 ( 6 6 X + 5 XY ) 7 + X XY 0.27 ) 1 Simplify Y = 1 1 + k 2 k 1 ( 7 + X XY 7 C A 0 ) 0.7 ( 6 6 X + 5 XY ) 0.27 ( 1 X ) 0.43 By Using Excel solver, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Yield Vs Conversion Conversion, X Yield, Y 3.2. Economic Potential
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